Suppose an unfair coin comes up heads 52.5% of the time if it is flipped. If the coin is flipped 16 times, what is the probability that: a) it comes up tails exactly 8 times? b) it comes up heads less than 4 times? Solution Using the binomial theorem P(x=8)= 16!/8!*8! (.525)^8(1-.525)^8= 0.1925 P(x=0)= (.475)^16 essentially nil P(x=1) 16 * (.525)*.475^15= 0.000118 P(x=2) 120*(.525)^2 *.475^14= 0.000984 P(x=3) 560 (.525)^3 *.475^13= 0.0051 .0051+.000984+.000118= 0.0063.